Cartesian Isomorphisms are Symmetric Monoidal: A Justification of Linear Logic

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Journal of Symbolic Logic 64 (1):227-242 (1999)
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Abstract

It is proved that all the isomorphisms in the cartesian category freely generated by a set of objects can be written in terms of arrows from the symmetric monoidal category freely generated by the same set of objects. This proof yields an algorithm for deciding whether an arrow in this free cartesian category is an isomorphism.

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